The main types of existing piles are concrete piles and steel pipe (SP) piles. In addition, the methods usually adopted for driving the piles are hammering and rotary embedding (Inazumi et al., 2020a, 2021; Kuwahara et al., 2020). When an existing pile is removed, it is often under an undesirable condition, as shown in Figure 4, such as the arrangement of the existing piles is different from the drawing, the existing piles are not even, an existing pile has broken in the ground, the joint sections of an existing pile are bad and an existing pile was unexpectedly placed at an incline. In the future, it will become more and more necessary to remove existing piles buried under various conditions safely and securely.

Figure 4 Buried status of an existing pile: (a) snapped; (b) broken; (c) joint offset; (d) joint unbonded; (e) oblique pile; (f) pile spacing is narrow; (g) hypertrophy of cement milk

The construction procedure using a wire rope, which among all others is a general method for removing existing piles, is shown in Figure 5 and described in the following (Kuwahara et al., 2019).

1. The steel casing is set so that the centre of the casing is aligned with the core of the existing pile.

2. While discharging the drilling fluid (water or bentonite water), the casing is inserted by rotation.

3. After completing the insertion of the casing by rotation down to the specified depth, the casing is pulled up, a wire rope is inserted into the tip of the casing and the rope attached to the tip of the casing is set in the existing pile.

4. The filling material is injected into the draw hole while the existing pile is being pulled up. (If the existing pile is heavy, it should be lifted with multiple heavy equipment and the top of the pile is cut off to decrease the weight.)

Figure 5 Construction procedure for the method of removing an existing pile using a wire rope

However, this removal method has some shortcomings, as shown in Figure 6. Firstly, when piles are buried under the undesirable conditions shown in Figure 4, it is difficult to remove them reliably with this method. Next, when injecting the filling material into a draw hole, it is not possible to fill in the very deepest part of the hole because the filling material is injected from the surface of the ground, and thus, voids form easily in the ground. Finally, when pulling up the pile, the wire is pulled up vertically, so there is a risk that the wire will not be able to withstand the stress or that the pile may break in the middle.

Figure 6 Problems with the method of removing an existing pile using a wire rope: (a) leaving the broken pile underground; (b) incomplete injection; (c) sling rail wire breaks

As a removal method devised to overcome the aforementioned issues that are sometimes encountered with the general removal method, there is a removal method in which the tip of the pile is chucked and pulled out. The construction procedure for this method is shown in Figure 7 and described in the following (Kuwahara et al., 2019; Inazumi et al., 2020b, 2020c).

1. Using a backhoe, the ground is excavated until the top end of the existing pile is exposed.

2. The steel casing is set so as to enclose the top end of the existing pile.

3. The ground is excavated by the rotating casing, and the drilling fluid is discharged from the tip of the casing.

4. The chuck claws are projected inwards from the casing at the lower end of the existing pile.

5. With the existing pile enclosed by the casing, the pile is pulled up while the casing is rotating and the filling material is being injected from the tip of the casing.

Figure 7 Construction procedure for the removal method by chucking the tip of the existing pile

In this removal method, because the entire length of the existing pile is pulled up in the state of being enclosed by the casing, it is possible to pull out the existing pile reliably even under undesirable conditions. Moreover, because no wire rope is used, there is no risk of the existing pile being dropped or the heavy machinery overturning due to breakage.

It is thought that existing piles may break because the drilling fluid in the casing is circulated by the insertion of the casing by rotation and the torsional stress is loaded onto the existing piles (see Figure 3). In principle, when drilling with a casing in a removal method that uses a wire or chucking and the casing does not reach the tip of the existing pile, the existing pile does not separate from the ground but remains fixed to the supporting layers. In other words, the existing pile itself does not rotate. Only the drilling fluid rotates, such that torsional stress is loaded onto the existing pile. As the casing is gradually inserted by rotation, the stress generated by the insertion of the rotating casing in the pile direction is loaded through the drilling fluid. At the same time, the circulating volume of the drilling fluid with the casing increases, so the stress loaded onto the existing pile increases. It is thought that an existing pile will often not be able to withstand the stress and will break.

CAE is an alternative technology for large-scale experiments, conducted in a room or in situ, using prototypes that have been created in a study as part of a development process of ‘manufacturing’. In other words, ‘CAE’ is a general term for technology that simulates and analyses prototypes on a computer formed by computer-aided design (CAD) and so on, considering the site conditions (Chang, 2014; Inazumi et al., 2020c; Pan et al., 2016). At the same time, CAE may refer to computer-aided engineering work or its tools for prior examination, design, manufacturing and process design of construction methods and products. In the field of geotechnical engineering, CAE can be used to visualise the inside of the ground and the stress loaded on the inside of the ground and to understand experiments that would normally require huge costs and/or phenomena that would be difficult to reproduce. In addition, by performing appropriate post-processing, it is possible to communicate with other people in a visually easy-to-understand manner.

With the remarkable development of computer technology in recent years, a method of analysis called the particle method (PM) has been developed. Here, the finite-element method (FEM) and the difference method (DM) comprise the grid method, in which the space is divided into grids and a physical quantity is assigned to each grid as a variable for calculation (Yang et al., 2020). Unlike the FEM and DM, the PM does not use grids, but instead discretises the continuum as particles that move with each physical quantity at each calculation point in a Lagrangian manner. Thus far, Inazumi et al. (2018) used the distinct-element method (DEM) to calculate the amount of movement of each particle by expressing the interacting stress between particles using the spring constant, damping constant, friction coefficient and so on. The DEM was also applied to the reproduction and performance evaluation of removal methods for existing piles (Inazumi et al., 2018). In this study, the authors apply the MPS method (Hattori, 2015; Shakibaeini and Jin, 2012; Tanaka et al., 2018) to analyse the behaviour of fluid particles according to the equation of motion for fluids. The governing equations for the incompressible flow used in the analysis are the mass conservation law, Equation 1, and the momentum conservation law, Equation 2, considering surface tension.

$$\frac{D\rho }{Dt}=0$$

1

$$\frac{Du}{Dt}=-\frac{1}{\rho }\nabla P+\nu {\nabla }^2\mathit{u}+\mathit{g}+\frac{1}{\rho }\sigma \kappa \delta \mathit{n}$$

2

where ρ is the density of the fluid, u is the velocity vector, P is the pressure, v is the kinematic viscosity coefficient, g is the gravity vector, σ is the surface tension coefficient, κ is the curvature, δ is the delta function for the surface tension acting on the surface and n is the unit vector in the direction perpendicular to the surface.

In the MPS method, each differential operator (slope, divergence and Laplacian) of the governing equation, shown in Equation 2, is discretised by a weighting function (Hattori, 2015; Shakibaeini and Jin, 2012; Tanaka et al., 2018). The weighting function depends on the interparticle distance and the influence radius (2.1–4.1 times the interparticle distance) in each particle interaction model.

In this study, therefore, an MPS-CAE analysis is performed to evaluate the mechanism of the stress loaded onto an existing pile when the steel casing is inserted into the ground.

In the on-site removal work of existing piles, the space enclosed inside the casing and its surroundings are filled with drilling fluid because the casing is inserted by rotation while discharging drilling fluid from the tip of the casing. However, it is difficult to reproduce drilling holes with the MPS-CAE analysis while discharging drilling fluid from the tip of the casing, so the MPS-CAE analysis was performed from the state of being previously filled with drilling fluid. If the pile length of 16 m is filled with particles (calculation points), assumed as the drilling fluid, the number of particles will increase and the MPS-CAE analysis will take a long time. At least the existing pile length of 0.5–0.6 m should be filled with drilling fluid particles in the MPS-CAE analysis. Therefore, MPS-CAE was carried out as shown in Figures 8 and 9 in which the casing was inserted by rotation at a velocity of 0.5 m/min for 1 min in two cases: first, the case of the interval width between the casing and the existing pile being 0.1 m (i.e. when the interval space was filled with 8480 particles) and second, the case of the interval width between the casing and the existing pile being 0.3 m (i.e. when the interval space was filled with 36 000 particles). The particle size of the drilling fluid was set to 0.03 m. Regarding the distance of 0.03 m between particles, three particles were able to pass even when the interval width between the casing and the existing pile was 0.1 m, which was the smallest width.

Figure 8 Overview of setting target in MPS-CAE analysis

Figure 9 Top view of setting target in MPS-CAE analysis

The authors evaluated the effect of the insertion of the casing in the ground by rotation on the existing piles from the three viewpoints of the stress loaded onto the existing piles, the rate of stress propagating from the casing to the existing piles and the safety factor against the breakage of the existing piles.

In the calculation of the stress loaded onto an existing pile, it is assumed in the MPS-CAE analysis that 0.5 m of the pile head is exposed from the surface of the ground, as shown in Figure 10, and that the casing is inserted by rotation for 1 min. Therefore, the position of the stress loaded onto an existing pile is 1.0 m from the existing pile head.

Figure 10 Assumptions in estimation of the stress loaded onto an existing pile in MPS-CAE analysis

The stress loaded onto an existing pile (F) is obtained by adding the pressure term, the viscosity term, the surface tension term and the external force term and calculating them as the sum of the neighbouring particles, as indicated in the following equation:

$$\stackrel{\rightharpoonup }{F}=-{\displaystyle {\sum }_i{m}_i}\left(-\frac{1}{\rho }\nabla P_i+\mu {\nabla }^2\stackrel{\rightharpoonup }{u_i}+\nabla {\varnothing }_i+\overrightarrow{{\alpha }_{ϵxt, i}}\right)$$

3

In the case of torsion, the torsional moment is called torque (T). It is expressed as the following equation:

$$T=\frac{Fd}{2}$$

4

where F is the magnitude of the loaded stress and d is the distance to the loaded stress.

In the case of an existing PC pile, the second polar moment of the area (I _p) is obtained by multiplying the square of the distance to a certain small area (r) by the area of the small area and differentiating it over the entire cross-section (see the following equation).

$$I_{\text{p}}={\displaystyle \underset{0}{\overset{d/2}{\int }}{r}^2\left(2\pi r\text{d}r\right)}=2\pi {\displaystyle \underset{0}{\overset{d/2}{\int }}{r}^3\text{d}r}=2\pi {\left[\frac{r^4}{4}\right]}_0^{d/2}=\frac{\pi d^4}{32}$$

5

In the case of an existing SP pile, d is represented as D ⁴ − d ⁴, and therefore, the following equation is obtained:

$$I_{\text{p}}=\frac{\pi }{32}\left(D^4-d^4\right)$$

6

where D is the outer diameter and d is the inner diameter.

Using Equations 3–6, the torsional stress (τ) and the maximum torsional stress (τ _max) are given by the following equations:

$$\text{PC pile:\hspace{1em}}\tau =\frac{Td}{I_{\text{p}}}{\tau }_{\max }=\frac{Td}{2I_{\text{p}}}$$

7

$$\text{SP pile:\hspace{1em}}\tau =\frac{TD}{I_{\text{p}}}{\tau }_{\max }=\frac{TD}{2I_{\text{p}}}$$

8

It is confirmed whether the allowable shear stress of an existing pile can resist the torsional stress generated by the insertion of the casing in the ground by rotation (Nishino, 1987; Nixon and McRoberts, 1976). In this study, the allowable shear stress value is assumed as 0.875 N/mm² for existing PC piles and as 90.45 N/mm² for existing SP piles, referring to the publications by Nishino (1987) and Nixon and McRoberts (1976).

Figures 11 and 12 present the phenomenon of the stress loaded onto existing PC piles and existing SP piles, respectively, with a pile diameter of 0.6 m when the casing is inserted by rotation for 60 s. The figures show time t on the horizontal axis and stress F on the vertical axis, and the percentage is a numerical value representing how much stress is propagated to an existing pile from the value of the stress loaded onto the inside of the casing after 60 s. Considering Figures 11(a)–11(c) and 12(a)–12(c), for the existing PC piles and the existing SP piles, respectively, the magnitude of stress tends to increase proportionally as the value of the plastic viscosity of the drilling fluid increases. However, the propagation rate of the stress from the casing to the existing pile increases as the plastic viscosity of the drilling fluid decreases. This is because the drilling fluid itself has no viscous stress and has almost the same rheological characteristics as water, so the stress from the casing is considered to be propagated quickly. Comparing Figures 11(a)–11(c) and 12(a)–12(c), it is seen that lower values for the plastic viscosity of the drilling fluid are accompanied by greater stress propagation rates, but a smaller effect of the stress on the existing pile. However, higher values for the plastic viscosity of the drilling fluid are accompanied by smaller stress propagation rates from the casing, but a larger effect of the stress on the existing pile. Besides, in Figures 11(a)–11(c) and 12(a)–12(c), the interval width between the casing and the existing pile is approximately 0.1 m, but 100% of the stress generated from the casing does not become loaded onto the existing pile. Considering cases in which the plastic viscosities of the drilling fluid are the same, the stress propagation when the interval width between the casing and the existing pile is 0.3 m (see Figures 11(d)–11(f) and 12(d)–12(f)) is smaller than when the interval width is 0.1 m (see Figures 11(a)–11(c) and 12(a)–12(c)): about 50% or less.

Figure 11 Stress loaded onto an existing PC pile when the casing is inserted by rotation: (a) Case_PC_0.6_0.1_1; (b) Case_PC_0.6_0.1_100; (c) Case_PC_0.6_0.1_1000; (d) Case_PC_0.6_0.3_1; (e) Case_PC_0.6_0.3_100; (f) Case_PC_0.6_0.3_1000

Figure 12 Stress loaded onto an existing SP pile when the casing is inserted by rotation: (a) Case_SP_0.6_0.1_1; (b) Case_SP_0.6_0.1_100; (c) Case_SP_0.6_0.1_1000; (d) Case_SP_0.6_0.3_1; (e) Case_SP_0.6_0.3_100; (f) Case_SP_0.6_0.3_1000

Up to now, engineers have thought that ‘the greater the amount of drilling fluid in the interval between the casing and an existing pile, the greater the stress applied to the existing pile, which may lead to the destruction of the existing pile’. In this analysis, the stress applied to the inside of the casing also increases as the amount of drilling fluid increases. However, because of the effect of the interval width on the stress reaching the existing pile, it is considered that the stress becomes smaller when the stress reaches the existing pile.

The classification of the stress loaded onto existing piles is shown in Tables 6 and 7. In the MPS-CAE analysis, stress loading is defined as the sum of the viscosity term, pressure term, surface tension term and external stress term. From Tables 6 and 7, the viscosity term and pressure term are the stresses that are mainly loaded onto existing piles. As a mechanism of the stress loaded onto the existing piles at an on-site location, it is thought that when the casing is inserted into the ground by rotation, pressure from the drilling fluid is generated in the direction of the existing pile, and the insertion of the casing by rotation causes frictional stress at the boundary between the existing pile and the drilling fluid and generates torsional stress (see Figure 13). When summarised comprehensively, based on Tables 6 and 7, in the case of both existing PC pile and SP pile, when the value of the plastic viscosity of the drilling fluid is 1000 Pa s or less and the casing diameter is 0.1 m larger than the existing pile, an existing pile with a diameter of less than 30 cm is unlikely to break due to the insertion of the casing by rotation.

Table 7 Classification of stress loaded onto existing SP piles

Figure 13 Mechanism revealed by MPS-CAE analysis on torsional stress loaded onto an existing pile